Aerodynamics for Engineering Students (Seventh Edition) PDF
Preview Aerodynamics for Engineering Students (Seventh Edition)
Aerodynamics for Engineering Students Seventh Edition Aerodynamics for Engineering Students Seventh Edition E.L. Houghton P.W. Carpenter Steven H. Collicott Daniel T. Valentine AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEWYORK • OXFORD • PARIS • SANDIEGO SANFRANCISCO • SINGAPORE • SYDNEY • TOKYO Butterworth-HeinemannisanimprintofElsevier Butterworth-HeinemannisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright©2017ElsevierLtd.Allrightsreserved Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without permissioninwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthe Publisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearance CenterandtheCopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(other thanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusing anyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethods theyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhavea professionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliability foranyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,or fromanyuseoroperationofanymethods,products,instructions,orideascontainedinthematerialherein. MATLAB®isatrademarkofTheMathWorks,Inc.andisusedwithpermission.TheMathWorksdoesnot warranttheaccuracyofthetextorexercisesinthisbook.Thisbook’suseordiscussionofMATLAB®software orrelatedproductsdoesnotconstituteendorsementorsponsorshipbyTheMathWorksofaparticular pedagogicalapproachorparticularuseoftheMATLAB®software. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-08-100194-3 ForinformationonallButterworth-Heinemannpublications visitourwebsiteathttps://www.elsevier.com/ Publisher:ToddGreen AcquisitionEditor:StephenMerken EditorialProjectManager:NateMcFadden ProductionProjectManager:SujathaThirugnanaSambandam Designer:VictoriaPearson TypesetbyVTeX Preface This volume is intended for engineering students in introductory aerodynamics courses and as a reference useful for reviewing foundational topics for graduate courses. Prior completion of an introductory thermodynamics course will assist the studentwithunderstandingbestthesectionswhichincludecompressible(highspeed) flows. Four divisions in the volume present an introduction, fundamentals of fluid dy- namics,aerodynamicsofairfoils,bodies,andwings,andaerodynamicapplications. Thus the subject development in this edition begins with definitions and concepts, developstheimportantequationsofmotion,andthenexploresboundarylayers,the important flow along aircraft surfaces. Inclusion of basic thermodynamics leads to thetopicofcompressibleflows,includingsupersonicphenomena. Theequationsofmotionarethensimplifiedtostudyincompressibleflow,includ- ing the powerful theory known as potential flow. Potential flow is applied to low speedairfoilandwingtheory,generatinglessonswhichareactuallyapplicableasa foundationtobegintounderstandalmosteverycomplexairfoilandwing.Compress- ible flow models are then combined with flows over airfoils and wings to begin to understandhighspeedflight. Attention is then turned to the computations and applications of aerodynamics. Obviously aerodynamic design today relies extensively on computational methods. Thisisreflectedinpartinthisvolumebytheintroduction,whereappropriate,ofde- scriptions and discussions of relevant computational techniques. However, this text is aimed at providing the fundamental fluid dynamics or aerodynamics background necessaryforstudentstomovesuccessfullyintoadedicatedcourseoncomputation methodsorexperimentalmethods.Assuch,experienceincomputationaltechniques orexperimentaltechniquesarenotrequiredforacompleteunderstandingoftheaero- dynamicsinthisbook.Theauthorsurgestudentsonwardtosuchadvancedcourses andexcitingcareersinaerodynamics. ADDITIONAL RESOURCES Asetof.mfilesfortheMATLABroutinesinthebookareavailablebyvisitingthe book’s companion site at www.textbooks.elsevier.com/9780081001943. Instructors usingthetextforacoursemayaccessthesolutionsmanualandimagebankbyvisit- ingwww.textbooks.elsevier.comandfollowingtheonlineregistrationinstructions. xiv Preface ACKNOWLEDGMENTS The authors thank the following faculty, who provided feedback on this project throughsurveyresponses,reviewofproposal,and/orreviewofchapters: Dr.GoetzBramesfeld RyersonUniversity Dr.KursatKara KhalifaUniversity,AbuDhabi BrianLandrum,Ph.D UniversityofAlabamainHuntsville Dr.TorstenSchenkel SheffieldHallamUniversity,Sheffield,England Prof.ChelakaraS.Subramanian FloridaInstituteofTechnology DavidTucker NorthbrookCollege,Sussex,England BruceVu NASAKennedySpaceCenter ProfessorsCollicottandValentinearegratefulfortheopportunitytocontinuethe workofProfessorsHoughtonandCarpenterandthankJoeHayton,Publisher,forthe invitationtodoso.Inaddition,theprofessionaleffortsofSteveMerken,Acquisitions Editor, Nate McFadden, Developmental Editor, Sujatha Thirugnana Sambandam, Production Manager, and Victoria Pearson Esser, Designer are instrumental in the creationofthisseventhedition. Theproductsofone’seffortsareofcoursetheculminationofallofone’sexperi- enceswithothers.Foremostamongstthepeoplewhoaretobethankedmostwarmly forsupportareourfamilies.CollicottandValentinethankJennifer,Sarah,andRachel andMary,Clara,Zoe,andZachT.,respectively,fortheirloveandforthecountless joysthattheybringtous.OurProfessorsandstudentsoverthedecadesaremajorcon- tributorstoouraerodynamicsknowledgeandwearethankfulforthem.Theauthors sharetheirdeepgratitudeforGod’sboundlessloveandgraceforall. CHAPTER 1 Basic Concepts and Definitions “To work intelligently” (Orville and Wilbur Wright) “one needs to know the effects of variations incorporated in the surfaces....Thepressuresonsquaresaredifferentfromthose onrectangles,circles,triangles,orellipses....Theshapeof theedgealsomakesadifference.” fromTheStructureofthePlane–MurielRukeyser LEARNINGOBJECTIVES • Reviewthefundamentalprinciplesoffluidmechanicsandthermodynamics requiredtoinvestigatetheaerodynamicsofairfoils,wings,andairplanes. • Recalltheconceptsofunitsanddimensionandhowtheyareappliedtosolving andunderstandingengineeringproblems. • Learnaboutthegeometricfeaturesofairfoils,wings,andairplanesandhowthe namesforthesefeaturesareusedinaerodynamicscommunications. • Exploretheaerodynamicforcesandmomentsthatactonairfoils,wings,and airplanesandlearnhowwedescribetheseloadsquantitativelyindimensional formandascoefficients. • Determinetheconditionsforlongitudinallystable,steady,levelaircraftflight. • Reviewcontrol-volumeanalysisbyexaminingthemomentumtheoryofpropellers andhelicopterrotors. • Learnthefundamentalsofhydrostaticsandwhenthetopicappliesto aerodynamics. 1.1 INTRODUCTION Thestudyofaerodynamicsrequiresanumberofbasicdefinitions,includinganun- ambiguous nomenclature and an understanding of the relevant physical properties, related mechanics, and appropriate mathematics. Of course, these notions are com- montootherdisciplines,anditisthepurposeofthischaptertoidentifyandexplain AerodynamicsforEngineeringStudents.DOI:10.1016/B978-0-08-100194-3.00001-8 1 Copyright©2017ElsevierLtd.Allrightsreserved. 2 CHAPTER 1 Basic Concepts and Definitions thosethatarebasicandpertinenttoaerodynamicsandthataretobeusedinthere- mainderofthevolume. 1.1.1 Basic Concepts Thistextisanintroductoryinvestigationofaerodynamicsforengineeringstudents.1 Hence, we are interested in theory to the extent that it can be practically applied to solveengineeringproblemsrelatedtothedesignandanalysisofaerodynamicobjects. Thedesignofvehiclessuchasairplaneshasadvancedtothelevelwherewere- quirethewealthofexperiencegainedintheinvestigationofflightoverthepast100 years.Weplantoinvestigatethecleverapproximationsmadebythefewwholearned howtoapplymathematicalideasthatledtoproductivemethodsandusefulformulas to predict the dynamical behavior of “aerodynamic” shapes. We need to learn the strengthsand,moreimportant,thelimitationsofthemethodologiesanddiscoveries thatcamebeforeus. Althoughwehaveextensivearchivesofrecordedexperienceinaeronautics,there arestillmanyopportunitiesforadvancement.Forexample,significantadvancements can be achieved in the state of the art in design analysis. As we develop ideas re- lated to the physics of flight and the engineering of flight vehicles, we will learn thestrengthsandlimitationsofexistingproceduresandexistingcomputationaltools (commerciallyavailableorotherwise).Wewilllearnhowairfoilsandwingsperform andhowweapproachthedesignsoftheseobjectsbyanalyticalprocedures. Thefluidofprimaryinterestisair,whichisagasatstandardatmosphericcondi- tions.Weassumethatthedynamicsoftheaircanbeeffectivelymodeledintermsof the continuumfluid dynamics model2 incompressibleor simple-compressiblefluid. Air is a fluid whose local thermodynamic state we assume is described either by its mass density ρ = constant, or by the ideal gas law. In other words, we assume air behaves as either an incompressible or a simple-compressible medium, respec- tively. The concepts of a continuum, an incompressible substance, and a simple- compressiblegaswillbeelaboratedoninChapter4. The equation of state, known as the ideal gas law, relates two thermodynamic propertiestootherpropertiesand,inparticular,thepressure.Itis p =ρRT (1.1) where p is the thermodynamic pressure, ρ is mass density, T is absolute (thermo- dynamic) temperature, and the specific gas constant for air is R = 287 J/(kgK) or 1Ithaslongbeencommoninengineeringschoolsforanelementary,macroscopicthermodynamicscourse tobecompletedpriortoacompressible-flowcourse.Theportionsofthistextthatdiscusscompressible flowassumethatsuchacourseprecedesthisone,andthusthediscussionsassumesomeelementaryexpe- riencewithconceptssuchasinternalenergyandenthalpy. 2Thatis,airapproximatedasacontinuousformofmatter,whichissufficientlyaccurateformostformsof flightpropelledbyair-breathingengines. 1.1 Introduction 3 R =1716ft-lb/(slug°R)−1.Pressureandtemperaturearerelativelyeasytomeasure. For example, “standard” barometric pressure at sea level is p = 101,325Pascals, whereaPascal(Pa)is1N/m2.InImperialunitsthisis14.675psi,wherepsiislb/in2 and1psiisequalto6895Pa(notethat14.675psiisequalto2113.2lb/ft2).Thestan- dard temperature is 288.15 K (or 15°C, where absolute zero equal to −273.15°C is used). In Imperial units this is 519°R (or 59°F, where absolute zero equal to −459.67°Fisused).Substitutingintotheidealgaslaw,wegetforthestandardden- sityρ =1.225kg/m3inSIunits(andρ =0.00237slugs/ft3inImperialunits).This isthedensityofairatsealevelgiveninthetableofdataforatmosphericair;thetable forstandardatmosphericconditionsisprovidedinAppendixB. Thethermodynamicpropertiesofpressure,temperature,anddensityareassumed to be the properties of a mass-point particle of air at a location x(cid:2) = (x,y,z) in space at a particular instant in time, t. We assume the measurement volume to be sufficiently small to be considered a mathematical point. We also assume that it is sufficientlylargesothatthesepropertieshavemeaningfromtheperspectiveofequi- libriumthermodynamics.Andwefurtherassumethatthepropertiesarethesameas thosedescribedinacourseonclassicalequilibriumthermodynamics.Therefore,we assume that local thermodynamic equilibrium prevails within the mass-point parti- cleatxandt regardlessofhowfastthethermodynamicstatechangesastheparticle movesfromonelocationinspacetoanother.Thisisanacceptableassumptionforour macroscopic purposes because molecular processes are typically much faster than anychangesintheflowfieldweareinterestedinfromamacroscopicpointofview are. In addition, we invoke the continuum hypothesis, with which we assume that the air is a continuous form of matter rather than discrete molecules. Thus we can defineallflowpropertiesascontinuousfunctionsofpositionandtimeandthatthese functionsaresmooth,thatis,theirderivativesarecontinuous.Thisallowsustoapply differential integral calculus to solve partial differential equations that successfully modeltheflowfieldsofinterestinthiscourse.Inotherwords,predictionsbasedon the theory reported in this text have been experimentally verified. The Continuum Hypothesisisvalidformostatmosphericflightbecausetherearesomanymolecules perunitvolume(approximately1019cm−3 atsealevel)thatthemotionofanyindi- vidualmoleculecannotbesensed. Todevelopthetheory,thefundamentalprinciplesofclassicalmechanicsareas- sumed.Theyare • Conservationofmass • Newton’ssecondlawofmotion • Firstlawofthermodynamics • Secondlawofthermodynamics Theprincipleofconservationofmassdefinesamass-pointparticle,whichisafixed- massparticle.Thustheprinciplealsodefinesmassdensityρ,whichismassperunit volume.Ifamass-pointparticleconservesmass,aswehavepostulated,thendensity changescanonlyoccurifthevolumeoftheparticlechanges,becausethedimension 4 CHAPTER 1 Basic Concepts and Definitions ofmassdensityisM/L3,whereMismassandLislength.TheSIunitofdensityis thuskg/m3. Avehiclemovingthroughtheairorairinmotionaroundthevehicleareofcourse causesofourstudyofthetopicofaerodynamics.Itisnaturalforthestudentreading this text to wish to get started quickly into a study of such motion. Aerodynamics, and fluid dynamics in general, are richly non-linear and thus, are rarely simple and quickstudies.However,thestudentwillfindoneimportantconceptinfluidmotion developed in Section2.2.1 and that concept is a relationship between pressure and velocity known as Bernoulli’s equation. It can be written in several forms, but here consideritthisway: 1 p =p+ ρV2 (1.2) o 2 Here the left side, p , is known by the synonyms “total pressure” and “stagnation o pressure.” In many, but not all, of the simple flows a student encounters, this total pressureisconserved—itisaconstant.Inthesecases,andalongastreamlineinsome more complex flows, the two terms on the right hand side must sum to a constant. The first term on the right is the static pressure, generally just called pressure. For pressuretobereduced,suchasoverthetopofanairfoilorwing,thesecondtermon therightsidemustbecomegreater.Becauseinlow-speedaerodynamicsthedensity isconstant,anyincreaseinthemagnitudeofthesecondtermiscausedbyanincrease in air velocity, V. Even when Bernoulli’s equation is not quantitatively correct for a certain situation, the energy exchange between static pressure and velocity of the flowexists. Studentsshouldapplythisequationwithcarewhilelearning,insubsequentSec- tions and Chapters, the conditions under which Bernoulli’s equation can be used properly. Newton’ssecondlawdefinestheconceptofforceintermsofacceleration(F(cid:2) = ma(cid:2)). The acceleration of a mass-point particle is the change in its velocity with re- specttoachangeintime.LetthevelocityvectorV(cid:2) = (u,v,w);thisisthevelocity of a mass-point particle at a point in space, x(cid:2) = (x,y,z), at a particular instant in timet.Theaccelerationofthismass-pointparticleis (cid:2) (cid:2) a(cid:2) = DV = ∂V +V(cid:2) ·∇V(cid:2) (1.3) Dt ∂t Thisisknownasthesubstantialderivativeofthevelocityvector.Sinceweareinter- estedinthepropertiesatfixedpointsinspaceinacoordinatesystemattachedtothe objectofinterest(i.e.,the“laboratory”coordinates),therearetwopartstomass-point particleacceleration.Thefirstisthelocalchangeinvelocitywithrespecttotime.The secondtakesintoaccounttheconvectiveaccelerationassociatedwithachangeinve- locityofthemass-pointparticlefromitslocationupstreamofthepointofinterestto theobservationpointx(cid:2)attimet. We will also be interested in the spatial and temporal changes in any property f of a mass-point particle of fluid. These changes are described by the substantial
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